- 9.1.1: Plot the point whose rectangular coordinates are 13, -12. What quad...
- 9.1.2: To complete the square of x2 + 6x, add . (pp. A28A29)
- 9.1.3: If P = 1a, b2 is a point on the terminal side of the angle u at a d...
- 9.1.4: tan-1 1 -12 = . (pp. 447449)
- 9.1.5: The origin in rectangular coordinates coincides with the in polar c...
- 9.1.6: True or False In the polar coordinates (r, u), r can be negative.
- 9.1.7: True or False The polar coordinates of a point are unique.
- 9.1.8: If P is a point with polar coordinates (r, u), the rectangular coor...
- 9.1.9: In 916, match each point in polar coordinates with either A, B, C, ...
- 9.1.10: In 916, match each point in polar coordinates with either A, B, C, ...
- 9.1.11: In 916, match each point in polar coordinates with either A, B, C, ...
- 9.1.12: In 916, match each point in polar coordinates with either A, B, C, ...
- 9.1.13: In 916, match each point in polar coordinates with either A, B, C, ...
- 9.1.14: In 916, match each point in polar coordinates with either A, B, C, ...
- 9.1.15: In 916, match each point in polar coordinates with either A, B, C, ...
- 9.1.16: In 916, match each point in polar coordinates with either A, B, C, ...
- 9.1.17: In 1730, plot each point given in polar coordinates
- 9.1.18: In 1730, plot each point given in polar coordinates
- 9.1.19: In 1730, plot each point given in polar coordinates
- 9.1.20: In 1730, plot each point given in polar coordinates
- 9.1.21: In 1730, plot each point given in polar coordinates
- 9.1.22: In 1730, plot each point given in polar coordinates
- 9.1.23: In 1730, plot each point given in polar coordinates
- 9.1.24: In 1730, plot each point given in polar coordinates
- 9.1.25: In 1730, plot each point given in polar coordinates
- 9.1.26: In 1730, plot each point given in polar coordinates
- 9.1.27: In 1730, plot each point given in polar coordinates
- 9.1.28: In 1730, plot each point given in polar coordinates
- 9.1.29: In 1730, plot each point given in polar coordinates
- 9.1.30: In 1730, plot each point given in polar coordinates
- 9.1.31: In 3138, plot each point given in polar coordinates, and find other...
- 9.1.32: In 3138, plot each point given in polar coordinates, and find other...
- 9.1.33: In 3138, plot each point given in polar coordinates, and find other...
- 9.1.34: In 3138, plot each point given in polar coordinates, and find other...
- 9.1.35: In 3138, plot each point given in polar coordinates, and find other...
- 9.1.36: In 3138, plot each point given in polar coordinates, and find other...
- 9.1.37: In 3138, plot each point given in polar coordinates, and find other...
- 9.1.38: In 3138, plot each point given in polar coordinates, and find other...
- 9.1.39: In 3954, the polar coordinates of a point are given. Find the recta...
- 9.1.40: In 3954, the polar coordinates of a point are given. Find the recta...
- 9.1.41: In 3954, the polar coordinates of a point are given. Find the recta...
- 9.1.42: In 3954, the polar coordinates of a point are given. Find the recta...
- 9.1.43: In 3954, the polar coordinates of a point are given. Find the recta...
- 9.1.44: In 3954, the polar coordinates of a point are given. Find the recta...
- 9.1.45: In 3954, the polar coordinates of a point are given. Find the recta...
- 9.1.46: In 3954, the polar coordinates of a point are given. Find the recta...
- 9.1.47: In 3954, the polar coordinates of a point are given. Find the recta...
- 9.1.48: In 3954, the polar coordinates of a point are given. Find the recta...
- 9.1.49: In 3954, the polar coordinates of a point are given. Find the recta...
- 9.1.50: In 3954, the polar coordinates of a point are given. Find the recta...
- 9.1.51: In 3954, the polar coordinates of a point are given. Find the recta...
- 9.1.52: In 3954, the polar coordinates of a point are given. Find the recta...
- 9.1.53: In 3954, the polar coordinates of a point are given. Find the recta...
- 9.1.54: In 3954, the polar coordinates of a point are given. Find the recta...
- 9.1.55: In 5566, the rectangular coordinates of a point are given. Find pol...
- 9.1.56: In 5566, the rectangular coordinates of a point are given. Find pol...
- 9.1.57: In 5566, the rectangular coordinates of a point are given. Find pol...
- 9.1.58: In 5566, the rectangular coordinates of a point are given. Find pol...
- 9.1.59: In 5566, the rectangular coordinates of a point are given. Find pol...
- 9.1.60: In 5566, the rectangular coordinates of a point are given. Find pol...
- 9.1.61: In 5566, the rectangular coordinates of a point are given. Find pol...
- 9.1.62: In 5566, the rectangular coordinates of a point are given. Find pol...
- 9.1.63: In 5566, the rectangular coordinates of a point are given. Find pol...
- 9.1.64: In 5566, the rectangular coordinates of a point are given. Find pol...
- 9.1.65: In 5566, the rectangular coordinates of a point are given. Find pol...
- 9.1.66: In 5566, the rectangular coordinates of a point are given. Find pol...
- 9.1.67: In 6774, the letters x and y represent rectangular coordinates. Wri...
- 9.1.68: In 6774, the letters x and y represent rectangular coordinates. Wri...
- 9.1.69: In 6774, the letters x and y represent rectangular coordinates. Wri...
- 9.1.70: In 6774, the letters x and y represent rectangular coordinates. Wri...
- 9.1.71: In 6774, the letters x and y represent rectangular coordinates. Wri...
- 9.1.72: In 6774, the letters x and y represent rectangular coordinates. Wri...
- 9.1.73: In 6774, the letters x and y represent rectangular coordinates. Wri...
- 9.1.74: In 6774, the letters x and y represent rectangular coordinates. Wri...
- 9.1.75: In 7582, the letters r and u represent polar coordinates. Write eac...
- 9.1.76: In 7582, the letters r and u represent polar coordinates. Write eac...
- 9.1.77: In 7582, the letters r and u represent polar coordinates. Write eac...
- 9.1.78: In 7582, the letters r and u represent polar coordinates. Write eac...
- 9.1.79: In 7582, the letters r and u represent polar coordinates. Write eac...
- 9.1.80: In 7582, the letters r and u represent polar coordinates. Write eac...
- 9.1.81: In 7582, the letters r and u represent polar coordinates. Write eac...
- 9.1.82: In 7582, the letters r and u represent polar coordinates. Write eac...
- 9.1.83: In Chicago, the road system is set up like a Cartesian plane, where...
- 9.1.84: Show that the formula for the distance d between two points P1 = 1r...
- 9.1.85: In converting from polar coordinates to rectangular coordinates, wh...
- 9.1.86: Explain how you proceed to convert from rectangular coordinates to ...
- 9.1.87: Explain how you proceed to convert from rectangular coordinates to ...
Solutions for Chapter 9.1: Polar Coordinates
Full solutions for Precalculus Enhanced with Graphing Utilities | 6th Edition
ISBN: 9780132854351
Solutions for Chapter 9.1
27
2
Since 87 problems in chapter 9.1: Polar Coordinates have been answered, more than 77742 students have viewed full step-by-step solutions from this chapter. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 9.1: Polar Coordinates includes 87 full step-by-step solutions.
Key Math Terms and definitions covered in this textbook
-
Affine transformation
Tv = Av + Vo = linear transformation plus shift.
-
Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).
-
Column space C (A) =
space of all combinations of the columns of A.
-
Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax - x Tb over growing Krylov subspaces.
-
Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].
-
Diagonal matrix D.
dij = 0 if i #- j. Block-diagonal: zero outside square blocks Du.
-
Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).
-
Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.
-
Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.
-
Left inverse A+.
If A has full column rank n, then A+ = (AT A)-I AT has A+ A = In.
-
Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.
-
Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n- l +Ln- 2 = A1 +A~, with AI, A2 = (1 ± -/5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.
-
Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.
-
Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.
-
Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.
-
Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)-l has AA+ = 1m.
-
Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·
-
Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.
-
Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.
-
Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.